Abstract: We perform a model-independent fit of the short-distance couplings
$C_{7,9,10}$ within the Standard Model set of $b\to s\gamma$ and $b\to
s\bar\ell\ell$ operators. Our analysis of $B \to K^* \gamma$, $B \to K^{(*)}
\bar\ell\ell$ and $B_s \to \bar\mu\mu$ decays is the first to harness the full
power of the Bayesian approach: all major sources of theory uncertainty
explicitly enter as nuisance parameters. Exploiting the latest measurements,
the fit reveals a flipped-sign solution in addition to a Standard-Model-like
solution for the couplings $C_i$. Each solution contains about half of the
posterior probability, and both have nearly equal goodness of fit. The Standard
Model prediction is close to the best-fit point. No New Physics contributions
are necessary to describe the current data. Benefitting from the improved
posterior knowledge of the nuisance parameters, we predict ranges for currently
unmeasured, optimized observables in the angular distributions of $B\to K^*(\to
K\pi)\,\bar\ell\ell$.